To prepare the burgers:
Shape the meat firmly into 4 round uniform patties about 1 1/2inches thick. Make a small indentation in the center of each patty and place 1 cube of the cheese in each. Knead the meat slightly to cover the hole. Brush both sides of the burgers lightly with the olive oil and season with salt and pepper to taste. Heat a large cast iron skillet over medium high heat until just smoking. Cook the burgers to your liking. Brush the apples on both sides with the vegetable oil. Grill (in a grill pan) until golden on both sides. Place a burger on the bottom of each roll, top with 1 or 2 apple slices and a dollop of ketchup
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